What is (3x)/(2x-3)-3/(x+6) ?

The solution to (3x)/(2x-3)-3/(x+6) is (3x^2+12x+9)/((x+6)(2x-3))

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simplify (3x)/(2x-3)-3/(x+6)

simplify

\frac{3 x}{2 x - 3} - \frac{3}{x + 6}

\frac{3 x ^{2} + 12 x + 9}{( x + 6 ) ( 2 x - 3 )}

Solution steps

\frac{3 x}{2 x - 3} - \frac{3}{x + 6}

Least Common Multiplier of

2 x - 3, x + 6 : (x + 6) (2 x - 3)

Adjust Fractions based on the LCM

= \frac{3 x ( x + 6 )}{( x + 6 ) ( 2 x - 3 )} - \frac{3 ( 2 x - 3 )}{( x + 6 ) ( 2 x - 3 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{3 x ( x + 6 ) - 3 ( 2 x - 3 )}{( x + 6 ) ( 2 x - 3 )}

Simplify

3 x (x + 6) - 3 (2 x - 3) : 3 x^{2} + 12 x + 9

= \frac{3 x ^{2} + 12 x + 9}{( x + 6 ) ( 2 x - 3 )}

8 (x + 1) - 12 x

(3 + 1)^{3}

\frac{4}{4 4}

1.151 7^{2}

- 4 (- 10 x - 1)

What is (3x)/(2x-3)-3/(x+6) ?
The solution to (3x)/(2x-3)-3/(x+6) is (3x^2+12x+9)/((x+6)(2x-3))